Question: Solve for $x$ and $y$ using elimination. ${-2x+3y = -8}$ ${3x-3y = 18}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-2x+3y = -8}\thinspace$ to find $y$ ${-2}{(10)}{ + 3y = -8}$ $-20+3y = -8$ $-20{+20} + 3y = -8{+20}$ $3y = 12$ $\dfrac{3y}{{3}} = \dfrac{12}{{3}}$ ${y = 4}$ You can also plug ${x = 10}$ into $\thinspace {3x-3y = 18}\thinspace$ and get the same answer for $y$ : ${3}{(10)}{ - 3y = 18}$ ${y = 4}$